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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 121242bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121242.s1 | 121242bc1 | \([1, 1, 1, -3442392, 1648575897]\) | \(2546528731011355033/809788299623424\) | \(1434589369869172644864\) | \([]\) | \(8064000\) | \(2.7634\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121242bc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 121242bc do not have complex multiplication.Modular form 121242.2.a.bc
sage: E.q_eigenform(10)